Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds

For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to the representation given by the composition of the lift of the holonomy representation defined by \eta, and the n-dimensional, irreducible, complex representation of SL(2,C). In the present work, we focus on two aspects of this invariant: its asymptotic behavior and its relationship with the complex-length spectrum of the manifold. Concerning the former, we prove that for suitable spin structures, log(\tau_n(M; \eta)) grows as -n^2 Vol(M)/4\pi, extending thus the result obtained by W. Mueller for the compact case. Concerning the latter, we prove that the sequence {\tau_n(M; \eta)} determines the complex-length spectrum of the manifold up to complex conjugation

Advanced measurement techniques for the characterization of ReRAM devices

In some Resistive Random Access Memories (ReRAM), which could become the next generation of non-volatile memories [1], the voltage-controlled high and low resistance states (HRS and LRS, respectively) are associated to the creation (Set) and disruption (Reset) of a conductive filament (CF) that locally connects (LRS) or disconnects (HRS) the electrodes [2]. Usually, a current limit (CL) must be fixed during the Set process. Typically, these devices are characterized using source measurement units (SMU) to measure the current through the device. However, most of the SMU have a low sampling rate (around 1sample/1ms) and the current limitation mechanism used by the equipment is not well understood. To overcome these limitations, in this work, a low-cost setup with large sampling rate (larger than 1sample/10μs) is presented which, in addition, includes a well-controlled wide-range current limiting unit, CLCU (Fig. 1). The system is suitable to capture fast transients during the Set/Reset processes (Fig. 2) and to detect HRS Random Telegraph Noise (RTN) unresolvable by SMUs (Fig. 3) [3]. These device-level measurements can be combined with a Conductive Atomic Force Microscope, to get information on CF properties that cannot be directly measured at device level, as, for example, the spatial distribution of current in the CF at LRS and HRS (Fig. 4) [4]. Please click Additional Files below to see the full abstract

Degradation of polycrystalline HfO2-based gate dielectrics under nanoscale electrical stress

The evolution of the electrical properties of HfO2/SiO2/Si dielectric stacks under electrical stress has been investigated using atomic force microscope-based techniques. The current through the grain boundaries (GBs), which is found to be higher than thorough the grains, is correlated to a higher density of positively charged defects at the GBs. Electrical stress produces different degradation kinetics in the grains and GBs, with a much shorter time to breakdown in the latter, indicating that GBs facilitate dielectric breakdown in high-k gate stacks

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

Breakdown-induced negative charge in ultrathin SiO2 films measured by atomic force microscopy

Atomic-force-microscopy-based techniques have been used to investigate at a nanometer scale the dielectric breakdown (BD) of ultrathin (<6 nm) SiO2films of metal-oxide-semiconductordevices. The results show that BD leads to negative charge at the BD location and the amount of created charge has been estimated. Moreover, the comparison of the charge magnitude generated during current-limited stresses and stresses without current limit demonstrates that the observed BD induced negative charge is related to the structural damage created by the oxide BD

Non-homogeneuos conduction of conductive filaments in Ni/HfO2/Si resistive switching structures observed with CAFM

Altres ajuts: ERDF/TEC2011-2792-C02-02Conductive filaments (CFs) in Ni/HfO₂/Si resistive switching structures are analysed at the nanoscale by means of Conductive Atomic Force Microscopy (CAFM). Differences in the CF conductivity are measured depending on the resistive state of the device. Moreover, for both resistance states, non-homogeneous conduction across the CF area is observed, in agreement with a tree-shaped CF

Nanoscale conductive pattern of the homoepitaxial AlGaN/GaN transistor

The gallium nitride (GaN)-based buffer/barrier mode of growth and morphology, the transistor electrical response (25–310 °C) and the nanoscale pattern of a homoepitaxial AlGaN/GaN high electron mobility transistor (HEMT) have been investigated at the micro and nanoscale. The low channel sheet resistance and the enhanced heat dissipation allow a highly conductive HEMT transistor ( I ds > 1 A mm −1 ) to be defined (0.5 A mm −1 at 300 °C). The vertical breakdown voltage has been determined to be ∼850 V with the vertical drain-bulk (or gate-bulk) current following the hopping mechanism, with an activation energy of 350 meV. The conductive atomic force microscopy nanoscale current pattern does not unequivocally follow the molecular beam epitaxy AlGaN/GaN morphology but it suggests that the FS-GaN substrate presents a series of preferential conductive spots (conductive patches). Both the estimated patches density and the apparent random distribution appear to correlate with the edge-pit dislocations observed via cathodoluminescence. The sub-surface edge-pit dislocations originating in the FS-GaN substrate result in barrier height inhomogeneity within the HEMT Schottky gate producing a subthreshold current

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)